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Journal of Materials Processing Technology 192–193 (2007) 1–7

Process design for closed-die forging of bevel gearby finite element analyses

J.-H. Song a, Y.-T. Im b,∗a Metallurgical Engineering Lab, R&D Division, Korea Automotive Technology Institute, 74 Yongjung-Ri, Pungse-Myun,

Chonan, Chungnam 330-912, South Koreab Computer Aided Materials Processing Laboratory, Department of Mechanical Engineering, ME3227,

Korea Advanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon 305-701, South Korea

bstract

In this study, process design for closed-die forging of a bevel gear used for a component of automobile transmission was made using three-imensional finite element simulations. Process variables of the closed-die forging of the bevel gear were selected to be the pressing type, punchocation, and billet diameter. Based on FE simulation results, appropriate process design without causing under-filling and folding defect wasetermined. In addition, with design of a die set including die insert and stress ring, cold forging of the bevel gear was experimented to estimateffectiveness of the designed process. From experiments, it was found that bevel gear with complete formation of the teeth was obtained without

aking any forming defects although flash in a forged product and punch fracture was occurred due to a slight difference in the punch stroke during

ormation. Through comparison of results between experiments and FE simulations, it was found that die clamping device should be modified forncrease of the clamping force and improvement of the die safety. 2007 Elsevier B.V. All rights reserved.

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eywords: Bevel gear; Closed-die forging; Process design; Die design; Finite e

. Introduction

Differential bevel gears, widely used as a component of auto-obile transmission, have been conventionally manufactured byachining. However, with increase of the market demand on

eduction of the production cost, cold forging has been grad-ally applied as an alternative method of machining. It hasompetitive advantages such as good surface finish, improvedechanical properties, and dimensional accuracy of the formed

roducts. Especially, closed-die forging in near-net-shape haseen well known as an effective process in reducing manufac-uring costs. However, since closed-die forging has high riskf causing under-filling or die fracture due to higher formingoad and die clamping force required during deformation, skill-ul process and die design is required to achieve productivity

nd competitiveness of the process.

With advancement of computing technologies, for reducingevelopment time and cost, computer aided engineering such as

∗ Corresponding author at: CAMP National Research Laboratory, Southorea. Tel.: +82 42 869 3227; fax: +82 42 869 3210.

E-mail address: ytim@kaist.ac.kr (Y.-T. Im).

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924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2007.04.081

nt analysis

nite element (FE) analysis and process design system has beenctively introduced in the field of metal forming. The FE anal-sis provides a die designer with various forming knowledgeuch as material behavior, distribution of stress and strain, andlastic deformation of dies without experiments. Thus, manyesearchers, Doege and Nagele [1], Szentmihali et al. [2], and

amalis et al. [3] have paid attention to application of FEimulations in gear manufacturing. Also, in order to apply a pro-ess design system in gear manufacturing, Song and Im [4,5]ave determined a major design parameter predicting the riskf under-filling of a tooth die cavity in the spur gear extrusionhrough three-dimensional FE simulations. They developed therocess design system with rule-base using major design param-ters. However, there have been rare studies reported regardinghe process design of bevel gears.

In this study, process design for closed-die forging of theevel gear was carried out using three-dimensional finite elementimulations and experiments. To achieve this, for a sphericalevel gear with teeth number 10, the pressing type, punch loca-

ion, and billet diameter were determined as process variables ofhe closed-die forging and influence of determined variables onormability of the product was investigated through FE simula-ions. Based on the uni-directional forging among the designed

2 Processing Technology 192–193 (2007) 1–7

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J.-H. Song, Y.-T. Im / Journal of Materials

rocesses predicted as the defect-free process through FE simu-ations, a cold forging die set including die insert and stress ringas designed using an empirical die design equation.Cold forging of the bevel gear with the billet material of

ISI1020 was experimented to estimate effectiveness of theesigned process as well. From experiments, it was found thathe bevel gear with complete formation of the teeth was obtainedithout forming a defect in the workpiece through the designed

losed-die forging process. However, flash in forged gear andunch fracture were occurred due to the mismatch of the punchtroke during formation. Finally, through comparison of resultsetween experiments and FE simulations, a relationship betweenhe punch stoke and die expansion force was estimated and it wasound that an additional clamping device increasing die clamp-ng forces was needed to improve the die safety. The presentpproach will be useful for practical use in industry.

. Process design using FE simulations

.1. Geometry of the bevel gear

In this study, the bevel gear product used as a componentf the automobile transmission was determined for the closed-ie forming process design. Fig. 1 shows the specification andimension of the bevel gear selected, of which teeth number,odule, and pressure angle were 10◦, 5.08◦, and 22.5◦, respec-

ively. Also, lower surface of the gear was in a spherical shapehile its upper surface was flat. Maximum diameter and holeiameter of the gear were 56.9 and 19.2 mm, respectively. Forhe selected bevel gear, process design according to the selectedrocess variables for the cold closed-die forming was carriedut.

.2. Process design

In this study, the pressing type, punch location, and initialillet diameter were selected as process variables for the closed-ie forging of the bevel gear. Inner hole of the gear product was

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Fig. 2. Designed processes for the closed-die forging of

ig. 1. Specification and dimension of the bevel gear selected for the closed-dieorming process design.

ssumed to be manufactured by trimming after cold formingas performed. Thus, in the process design, punch and lowerie were designed to have protruded geometry for the sake ofonvenience of trimming process and material saving. Heightf protruded geometry was decided to prevent direct contactetween the initial billet with teeth profile of dies at the initialorming stage.

Fig. 2 shows designed processes for the closed-die formingf bevel gears according to variation of process variables. Thenitially designed process was the uni-directional forming withhe billet diameter of 25 mm.

Based on the initially designed process, the processes weree-designed for the bi-directional forging with pressing the work-iece through the punch and ejector simultaneously. Also, inhe uni-directional forming, changing punch location to the flaturface of the product instead of the spherical surface of theroduct was carried out as well. Finally, the initial billet diame-

er was increased to 30 and 35 mm, respectively. For the designedrocesses, the influence of process variables on formability ofhe workpiece was investigated through three-dimensional FEimulations in the present investigation.

the bevel gear for three-dimensional FE analyses.

ls Processing Technology 192–193 (2007) 1–7 3

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Fig. 3. Contour plots of the effective strain distribution of deformed workpieceobtained from FE analyses for (a) uni-directional and (a) bi-directional pressingforgings.

J.-H. Song, Y.-T. Im / Journal of Materia

.3. FE simulations

In this study, an in-house FE program CAMPform3D [6,7]as used to investigate formability of the designed processes. It

s composed of a solver based on the thermo-rigid-viscoplasticpproach and remeshing module adopting master grid approachnd octree based refinement algorithm [8–11]. Teeth profile ofhe spherical bevel gear was calculated from the geometric equa-ion reported from the literature [12] and its three-dimensionalie surface and triangular surface meshes were created using theommercialized program I-DEAS.

The workpiece used for analyses was AISI4130 whose mate-ial property was available in the report of ICFG [13]:

¯ = 900ε̄0.2 (MPa) (1)

ere σ̄ and ε̄ are the effective stress and strain, respectively.The punch velocity was assumed to be 1.0 mm/s. Considering

eometrically rotational symmetry, only half of the tooth wassed in simulations in order to save the simulation time. Constanthear friction factor 0.1 was used in simulations.

.3.1. Variation of the pressing typeComparison of the formability between uni-directional and

i-directional pressing forgings was carried out when the billetiameter was 25 mm. Fig. 3 shows the contour plot of the effec-ive strain distribution of the deformed workpiece predicted fromE analyses. Punch strokes of uni-directional and bi-directionalressing forgings were 40 and 20 mm, respectively, consideringhe punch and ejector moved simultaneously in the bi-directionalorming. In the uni-directional forging, folding defect of theorkpiece was predicted on the protruded region as the materialas deformed toward the die teeth region compared to better

ormability in the bi-directional forging.This was because the die cavity was efficiently filled up by

pset deformation of the workpiece occurred in the center ofeight.

In Fig. 3, it can be seen that the effective strain of the work-iece was symmetrically distributed in the bi-directional forgingnd maximum effective strain value of the workpiece in theni-directional forging was slightly higher than that in the bi-irectional forging. Fig. 4 shows comparisons of load–strokeurves obtained from FE analyses between bi-directional andni-directional forgings. As shown in this figure, stiff rising oforming loads was commonly observed according to increasef the punch stroke. The predicted maximum forming loadsf the punch in uni- and bi-directional forgings were 3012nd 2503 kN, respectively. Thus, it was construed that forma-ility of the bi-directional forming is better than that of theni-directional forming in terms of forming defect and load.

.3.2. Variation of the punch locationIn the uni-directional forging with the billet diameter 25 mm,

unch location was changed to the flat surface of the gear insteadf the spherical surface of the gear as shown in the second andhird in Fig. 2. Fig. 5 shows deformed shape of the workpiece pre-icted from the FE analysis when the punch stroke was 40 mm.

Fig. 4. Comparisons of load–stroke curves obtained from three-dimensional FEanalyses between bi-directional and uni-directional pressing forgings.

4 J.-H. Song, Y.-T. Im / Journal of Materials Processing Technology 192–193 (2007) 1–7

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ig. 5. Deformed shape of the workpiece when the punch was located on theat face of the product obtained from FE analyses.

s shown in this figure, folding phenomenon was observed onhe protruded region irrespective of the punch location. Also, athe end region of the flat surface of the upper die, folding defectas additionally observed because material flow toward the flat

urface was prevented as punch progresses. The predicted max-mum forming load was 2846 kN. Thus, in the uni-directionalorming, punch should be located at the spherical surface of theevel gear in order to reduce the load requirement.

.3.3. Variation of the billet diameterFig. 6 shows deformed shapes of the workpiece predicted

rom FE simulations when the billet diameter was (a) 30 mmnd (b) 35 mm, respectively. As shown in this figure, foldingefect observed in the case of the billet diameter 25 mm wasisappeared according to increase of the billet diameter. How-ver, when the billet diameter was 35 mm, under-filling at theottom of the protruded region was found due to increase of itseight. Thus, it was found that formability of the process coulde improved by changing the billet diameter.

Fig. 7 shows the force applied to dies and the punch predictedrom FE analyses according to variation of the billet diameters.n this figure, Fp and Fud are the forming load and die expansion

ig. 6. Deformed shapes of the workpiece obtained from FE simulations withhe billet diameters of (a) 30 mm and (b) 35 mm, respectively.

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ig. 7. Force applied to dies and the punch predicted from FE analyses accordingo variation of billet diameters.

orce at complete filling of the die cavity, respectively. In order tochieve complete formation without flash and die safety, clamp-ng device enduring die expansion force, Fud, was required. Inhis figure, the predicted forming loads in the case of the billetiameter of 30 and 35 mm were 3876 and 4789 kN, respectively.ince the punch area contacting with the workpiece was enlargedccording to increase of the billet diameter, forming load wasncreased as well. However, the required clamping force wasecreased due to reduction of the contact area between the work-iece and upper die. In case of the billet diameter of 30 mm, diexpansion force was predicted as 1.86 times of forming load.

. Die design for the closed-die forging

.1. Die design

In this study, die design was made for the designed uni-irectional process with the initial billet diameter of 30 mmhrough FE simulations. Fig. 8(a) shows the designed die setor the closed-die forging of the bevel gear, in which shrink fit-ing between die insert and stress ring was applied to improvehe die safety. Material type of the die insert, punch and ejec-or contacting with the workpiece was commonly decided to beISI M-2 having high yield strength in order to endure higher

orming pressures and minimize its elastic deformation. On thether hand, since stress ring has little influenced on gear forma-ion, its material type was selected to be AISI H-13. In order tondure die expansion force during formation, eight bolts with20 were used as the die clamping device.In the die design, the outer radius of the stress ring was

ecided to be three times of maximum radius of the gear. Also,he inner radius of the stress ring was decided from the followingmpirical equation:

Si =√

R × RSo (2)

ere R, RSi, and RSo are the average value between the billetadius and maximum radius of the gear, inner and outer radiusf the stress ring, respectively.

Since R and RSo were 21.5 and 87 mm, respectively, RSias designed to be 43 mm. In addition, a shrink fitting ratio,

atio between the shrink fitting value and inner radius of the

tress ring, was determined to be 0.45%. Fig. 8(b) shows thehotograph of the manufactured lower die with teeth profile forhe closed-die forging of the bevel gear based on the present dieesign. Bevel gear teeth of dies were manufactured by electrical

J.-H. Song, Y.-T. Im / Journal of Materials Processing Technology 192–193 (2007) 1–7 5

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pafthe experiment. As shown in this figure, due to the cracking atthe punch head, lower part of the punch was fitted at the upperdie.

ig. 8. (a) Designed die set and (b) photograph of the manufactured lower dieith teeth profile for the closed-die forging of bevel gear.

ischarging machine and grooves in the die were machined offor fastening bolts between the upper and lower dies.

.2. Experimental set-up

Experiments were carried out using the hydraulic press withhe limiting forming load of 400 t. Tooth die cavity was machinedhrough wire cutting and punches for hollow and solid gear extru-ions were separately manufactured. The relationship betweenhe forming load and punch stroke was measured using linearoltage displacement transducer and load cell.

. Results and discussion

In this study, the closed-die forging of the bevel gear wasxperimented in order to verify effectiveness of the designedrocess. AISI1020 was selected as the material type of the bil-et because of the limiting load of the hydraulic press used for

xperiments. Diameter and height of the billet were determinedo be 29.9 and 46 mm, respectively. With annealing of the bil-et, phosphate coating + MoS2 was used as a lubricant. Duringxperiments, careful control of the punch stroke should be made F

ig. 9. Photographs of cold forged shapes of bevel gear according to variationf punch strokes: (a) front view and (b) top view.

t the final forming stage in order to escape excessive increasef punch stroke resulted in stiff rise of forming loads.

Fig. 9 shows photographs of cold forged shapes of the bevelear according to variation of punch strokes. As shown in thisgure, teeth profile of the bevel gear was completely forgedithout folding or under-filling of the product. Final forming

oad was approximately 1863 kN. However, flash on the forgedear was formed due to elongation of bolts according to a slightlyarger punch stroke than the one required.

Also, as shown in Fig. 10, punch was fractured during theunch ejection due to mismatch of the center axis between uppernd lower dies. Fig. 11 shows photographs of the upper die withractured lower part of the punch and punch head fractured in

ig. 10. Drawing of the die and punch when the elongation of bolts was occurred.

6 J.-H. Song, Y.-T. Im / Journal of Materials Processing Technology 192–193 (2007) 1–7

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ig. 11. Photographs of (a) upper die with fractured lower part of the punch anevel gear.

In order to investigate die expansion force due to the excessiveunch stroke, FE simulation was carried out. In order to obtainaterial property of AISI1020, a simple upsetting was carried

ut for the specimen having the diameter 30 mm and height5 mm.

Fig. 12 shows the stress–strain curve measured from theimple upsetting test. Also, calibrated stress–strain equation ofISI1020 was determined as follows:

¯ = 649.23ε̄0.06 (MPa) (3)

ere σ̄ and ε̄ are the effective stress and strain, respectively.Fig. 13 shows the analysis condition and mesh layouts of

he workpiece and dies for the three-dimensional FE analysisf closed-die forging of bevel gear. The numbers of nodes andlements of the workpiece were 2759 and 2100, respectively,nd 1/10 model used to reduce the analysis time.

Constant shear friction factor was assumed to be 0.15 andaterial property obtained from the simple upset test was used.ig. 14(a) shows comparisons of the deformed shapes between

he experiment and FE simulation at the punch stroke 24.7 mm.eformed shape obtained from FE simulations was in good

greement with that obtained from experiments.Fig. 14(b) shows comparisons of the load–stroke curve

etween the experiment and FE simulation. Forming load pre-icted from the FE simulation matched well with that obtained

Fig. 12. Stress–strain curve through upset experiments for AISI1020.Fig. 14. Comparisons of (a) the deformed shapes and (b) load–stroke curvebetween the experiment and FE simulation.

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ig. 15. Forming load required and force applied to the upper die obtained fromhe three-dimensional FE analysis according to increase of the punch stroke.

rom experiments although the forming load predicted fromhe FE simulation was slightly higher than that obtained fromxperiments at the initial punch stroke.

Fig. 15 shows the required forming load and expansion forcepplied to the upper die predicted from the three-dimensional FEnalysis according to increase of the punch stroke. Consideringhat forming load obtained from experiments was 1863 kN at thenal forming stage, the upper die expansion force predicted from

he FE simulation was 1620 kN. Since maximum yielding forcef the bolt used in the dies clamping was 196 kN, designed totalie clamping force was 1568 kN. Thus, due to the slight mis-atch of the punch stroke, elongation of the bolt was occurred

nd increase of die clamping force was needed to improve theie safety.

. Conclusions

In the present study, process design for closed-die forging of

he bevel gear using three-dimensional FE simulations was car-ied out. As the process variables in the closed-die forging of theevel gear, the pressing type, punch location, and billet diame-er were used for investigating the material flow and load levels

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ocessing Technology 192–193 (2007) 1–7 7

equired for complete formation without causing any defects.ased on the process verified from FE simulations, the die set-p was designed and the bevel gear with the billet material ofISI1020 was cold forged. From experiments, the bevel gearith complete formation of teeth was obtained without formingefect in the workpiece with the designed process. However,ash in the forged gear and punch fracture was occurred due to

he over punch stroke during formation. Through comparisonf results between experiments and FE simulations, the rela-ionship between the punch stoke and die expansion force wasstimated and it was found that an additional clamping devicencreasing the die clamping force was needed to improve the dieafety. From this study, it was expected that designed processould be efficiently used in the bevel gear forging for practicalse in the related industry.

cknowledgement

The authors wish to thank the grant of National Researchaboratory of the Ministry of Science and Technology through

he Korea Science and Engineering Foundation, without whichhis work would not have been possible.

eferences

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Proc. Technol. 43 (1994) (1994) 279–291.[3] A.G. Mamalis, D.E. Manolakos, A.K. Baldoukas, J. Mater. Proc. Technol.

57 (1996) 164–171.[4] J.H. Song, Y.T. Im, Trans. ASME J. Manuf. Sci. Eng. 126 (2004) 255–

263.[5] J.H. Song, Y.T. Im, J. Mater. Proc. Technol. 153/154 (2004) 821.[6] S.Y. Kim, Y.T. Im, Int. J. Form. Proc. 3 (2000) 253–278.[7] S.Y. Kim, Y.T. Im, J. Mater. Proc. Technol. (2002) 57–63.[8] D.Y. Kwak, J.S. Cheon, Y.T. Im, Int. J. Numer. Meth. Eng. 53 (2002)

2463–2500.[9] D.Y. Kwak, Y.T. Im, Int. J. Numer. Meth. Eng. 53 (2002) 2501–2528.10] W.Y. Choi, D.Y. Kwak, I.H. Son, Y.T. Im, Int. J. Numer. Meth. Eng. 58

(2003) 1857–1872.11] I.H. Son, Y.T. Im, Int. J. Numer. Meth. Eng. 67 (2006) 672–696.12] M.J. AI-Daccak, J. Angeles, M.A.G. Palacios, Trans. ASME J. Mech. Des.

116 (1994) 364–368.13] International Cold Forging Group, Cold Forgeable Steels, 1996.